Complex Dynamics in Simplified Neuronal Models: Reproducing Golgi Cell Electroresponsiveness

Abstract

Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF model family and is therefore mono-compartmental, keeps the limited computational load typical of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model parameters and neuronal membrane mechanisms through a minimum set of equations. In order to test its potential, E-GLIF was used to model a specific neuron showing rich and complex electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole set of complex neuronal dynamics typical of these neurons – including intensity-frequency curves, spike-frequency adaptation, post-inhibitory rebound bursting, spontaneous subthreshold oscillations, resonance, and phase-reset – providing a new effective tool to investigate brain dynamics in large-scale simulations.

Reconstruction and Simulation of a Scaffold Model of the Cerebellar Network

“…Secondly, the scaffold could be used to evaluate the trade-off between computational efficiency and precision. Therefore, the present LIF single point neurons could be substituted by others (extended generalized LIF, E-GLIF) embedding non-linear firing properties (e.g., Brette and Gerstner, 2005; Geminiani et al, 2018) and accounting for synaptic dendritic location by modifying the transmission weight depending on the distance of synapses from the soma (Rössert et al, 2016) or based on experimental data when available.…”

Complex Electroresponsive Dynamics in Olivocerebellar Neurons Represented With Extended-Generalized Leaky Integrate and Fire Models

“…In previous work, E-GLIF proved able to generate the complete set of GoC spiking responses to different inputs, with a minimum number of equations and free parameters. This makes it the best candidate to be used in SNNs to optimize the compromise between biological plausibility and computational load (Geminiani et al, 2018).…”

“…The endogenous current, I e , accounts for autorhythm and regulation of the intrinsic steady-state membrane potential; the adaptive current, I adap , coupled with V m accounts for intrinsic sub-threshold oscillations of the membrane potential and represents the slow hyperpolarizing sub-cellular currents, e.g., the K + channel currents; the spike-triggered current, I dep , accounts for fast depolarizing mechanisms, e.g., the Na + and low threshold voltage activated Ca 2+ channel currents. For neuron connections within SNNs, conductance-based synapses are used, with spike-triggered change of synaptic conductance, g syn , according to an alpha function (Cavallari et al, 2014; Geminiani et al, 2018):…”

“…However, representing this rich set of electroresponsive patterns through simplified neuron models is fundamental to develop realistic multiscale Spiking Neural Networks (SNNs). To tackle this issue, we here exploited the Extended-Generalized Leaky Integrate and Fire (E-GLIF) point neuron that allows to model single-point neurons while keeping a realistic picture of multiple essential electrophysiological features such as autorhythm, bursting, adaptation, oscillations, and resonance (Geminiani et al, 2018). The E-GLIF, which was originally used to reproduce the GoC electroresponsiveness (Geminiani et al, 2018), was used here to optimize and test the other cerebellar neurons: GRs, PCs, MLIs, DCNs, and IO.…”

“…To tackle this issue, we here exploited the Extended-Generalized Leaky Integrate and Fire (E-GLIF) point neuron that allows to model single-point neurons while keeping a realistic picture of multiple essential electrophysiological features such as autorhythm, bursting, adaptation, oscillations, and resonance (Geminiani et al, 2018). The E-GLIF, which was originally used to reproduce the GoC electroresponsiveness (Geminiani et al, 2018), was used here to optimize and test the other cerebellar neurons: GRs, PCs, MLIs, DCNs, and IO. The results shown here are fundamental in view of SNNs simulations where the impact of complex single neuron dynamics will be evaluated at the network and, eventually, at the behavioral level (D’Angelo et al, 2016a).…”